Question

the function y = f(x) is graphed below. what is the average rate of change of the function f(x) on the interval -1 ≤ x ≤ 2?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ on the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$ and $b = 2$.

Step2: Read function values from graph

From the graph, when $x=-1$, $f(-1)\approx - 10$; when $x = 2$, $f(2)\approx-20$.

Step3: Calculate average rate of change

Substitute into the formula: $\frac{f(2)-f(-1)}{2-(-1)}=\frac{-20 - (-10)}{2 + 1}=\frac{-20 + 10}{3}=\frac{-10}{3}=-\frac{10}{3}$.

Answer:

$-\frac{10}{3}$